Highest Common Factor of 2658, 7748 using Euclid's algorithm
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 2658, 7748 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 2658, 7748 is 2 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 2658, 7748 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 2658, 7748 is 2.
HCF(2658, 7748) = 2
HCF of 2658, 7748 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2658, 7748 is 2.
Highest Common Factor of 2658,7748 is 2
Step 1: Since 7748 > 2658, we apply the division lemma to 7748 and 2658, to get
7748 = 2658 x 2 + 2432
Step 2: Since the reminder 2658 ≠ 0, we apply division lemma to 2432 and 2658, to get
2658 = 2432 x 1 + 226
Step 3: We consider the new divisor 2432 and the new remainder 226, and apply the division lemma to get
2432 = 226 x 10 + 172
We consider the new divisor 226 and the new remainder 172,and apply the division lemma to get
226 = 172 x 1 + 54
We consider the new divisor 172 and the new remainder 54,and apply the division lemma to get
172 = 54 x 3 + 10
We consider the new divisor 54 and the new remainder 10,and apply the division lemma to get
54 = 10 x 5 + 4
We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get
10 = 4 x 2 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2658 and 7748 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(54,10) = HCF(172,54) = HCF(226,172) = HCF(2432,226) = HCF(2658,2432) = HCF(7748,2658) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 2658, 7748 using Euclid's Algorithm
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 2658, 7748?
Answer: HCF of 2658, 7748 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2658, 7748 using Euclid's Algorithm?
Answer: For arbitrary numbers 2658, 7748 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
